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    <center>Scilab Function</center>
    <div align="right">Last update : April 1993</div>
    <p>
      <b>bifish</b> -  shows a bifurcation diagram in a fish population discrete time model</p>
    <h3>
      <font color="blue">Calling Sequence</font>
    </h3>
    <dl>
      <dd>
        <tt>bifish([f_ch])  </tt>
      </dd>
    </dl>
    <h3>
      <font color="blue">Parameters</font>
    </h3>
    <ul>
      <li>
        <tt>
          <b>f_ch</b>
        </tt>: can be one of <tt>
          <b>fish</b>
        </tt>, <tt>
          <b>fishr</b>
        </tt> and <tt>
          <b>fishr2</b>
        </tt>. This option selects the population model.</li>
    </ul>
    <h3>
      <font color="blue">Description</font>
    </h3>
    <p>
    The dynamical system <tt>
        <b>fish</b>
      </tt> is the following :</p>
    <pre>

           y=b*exp(-0.1*(x(k)_1+x(k)_2));
           x(k+1)=[ y 2*y ; s 0.0]*x(k);
   
    </pre>
    <p>
    and the parameters <tt>
        <b>s</b>
      </tt> evolves to show the bifurcation diagram.
    <tt>
        <b>fishr</b>
      </tt> and <tt>
        <b>fishr2</b>
      </tt> are constructed as above but with added white noises.</p>
    <pre>

 fishr
 y=b*exp(-0.1*(xk(1)+xk(2))) 
 xkp1=[ y 2*y ; s*(1+0.1*(rand()-0.5)) 0.0]*xk

 fishr2
 z=exp(-0.1*(xk(1)+xk(2))) 
 xkp1=[ b*z**(1+0.1*(rand()-0.5)) 2*b*z**(1+0.1*(rand()-0.5)) ; s 0.0]*xk
   
    </pre>
    <p>
    The three macros <tt>
        <b>fish, fishr, fishr2</b>
      </tt> are loaded in Scilab when calling <tt>
        <b>bifish</b>
      </tt>.</p>
    <h3>
      <font color="blue">See Also</font>
    </h3>
    <p>
      <a href="../nonlinear/ode.htm">
        <tt>
          <b>ode</b>
        </tt>
      </a>,&nbsp;&nbsp;</p>
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